Martina Morris & Jeanette Birnbaum
To use CD4 data to increase the precision of undiagnosed estimates from the testing history model
Why
How
Impact in WA
The hazard (instantaneous rate) of infection at any point within the window is 1/(window length), shown by the red line for two different window lengths. Time=0 refers to time of diagnosis.
The red line is lower when the window is longer, since the probability of infection is spread out over a longer time period.
Cumulative probability of diagnosis is the area under the curve. At 1 year prior to diagnosis, for example, the 2-year window assigns greater probability of infection than the 4-year window.
Since 1 year is ½ of 2 years, 50% of infection probability occurs within 1 year for the 2-year window. In contrast, only ¼ or 25% of infection probability occurs within 1 year for the 4-year window.
For never-testers, we assume a window of 18 years or age-16, whichever is smaller.
Example of windows for never-testers of different ages
The age distribution of never-testers thus influences what window lengths they contribute to the population TID (time from infection to diagnosis).
Testing histories = Tested + Never Tested
Breakdown of testing histories in WA HIV cases 2005-2014.
Total N=5148
N with testing history N=3016.
Testing history breakdown by MSM status. Percents are within MSM status group. Total N=5148.
MSM comprise about 2/3 of cases.
What is driving differential response rates?
Distribution of infection window lengths in years (N=3016). Labels indicate bounds, e.g. (0,1] includes windows>0 and <=1. The 18-year windows imputed because of the assumption for never-testers are labeled as 18 (NT).
50% have windows between 0 and 2 years (red plus gold). Our assumption for never-testers almost doubles the number of windows >=5 years (blue plus purple).
Distribution of infection window lengths for non-MSM (top) and MSM. Percents are within MSM status groups.
The 18-year assumption for never-testers is almost 4x more common among non-MSM (31%) than among MSM (7%).
Percent of cases with a concurrent AIDS diagnosis at time of HIV diagnosis, by MSM status.
Age distribution of never-testers in WA 2005-2015, by MSM status (pink=MSM).
Mean age at diagnosis among never-testers is 42 in non-MSM, versus 36 in MSM
Remember the assumption for never-testers: window=min(age-16,18). Cases older than 16+18=34 will all have 18-year windows.
Whether it's using BED, CD4, or concurrent AIDS dx, etc
Increasing precision will not necessarily decrease undiagnosed estimates
Total population estimates will not change greatly, but our confidence in them will increase
| Window Length | If CD4 unknown, infection probability is mostly: |
|---|---|
| Short | Recent |
| Long | Non-recent |
| Window Length | If CD4 unknown, infection probability is mostly: | CD4=Low | CD4=High |
|---|---|---|---|
| Short | Recent | Recent (fast progressor?) | Recent |
| Long | Non-recent | Non-recent | Recent |
How to define “short” and “long”, “low” and “high”?
Years it takes for 50% of cases to reach CD4 level:
| CD4 Category | Lodi 2011 | Cori 2015 | Our approximation* |
|---|---|---|---|
| >500 | 1.19 | 2.3 | 1.5 |
| 350-500 | 4.19 | 4.17 | 4 |
| 200-350 | 7.93 | 7.98 | 8 |
| 0-200 | 11.5 | 9 |
* Simplified median times that are consistent with both sources. For CD4 0-200, we will retain our maximum-window assumption of 18 years. This sets a maximum median time of 9 years
Interpretation: 50% of infection probability should occur within the median time.
Implication: If a case has CD4>500 at diagnosis, for example, we expect 50% of his infection probability to occur in the 1.5 years prior to dx
Lodi S, Phillips A, Touloumi G, Geskus R, Meyer L, Thiébaut R, et al. Time from human immunodeficiency virus seroconversion to reaching CD4+ cell count thresholds <200, <350, and <500 Cells/mm3: assessment of need following changes in treatment guidelines. Clin Infect Dis Off Publ Infect Dis Soc Am. 2011 Oct;53(8):817–25
Cori A, Pickles M, van Sighem A, Gras L, Bezemer D, Reiss P, et al. CD4+ cell dynamics in untreated HIV-1 infection: overall rates, and effects of age, viral load, sex and calendar time. AIDS Lond Engl. 2015 Nov 28;29(18):2435–46.
Base Case: 50% infection probability is in each half of the window
In the example of a window of 18 years, 50% probability of infection is spread across years 0-9 prior to dx
CD4 Case: 50% of infection probability is shifted into the CD4-based median window
For a window of 18 years and various CD4 bins at diagnosis, the graphs show the Base Case (red) versus CD4 Case (blue) distribution of the probability of infection within the window. Shading indicates the new placement of 50% of infection probability.
| CD4 Category | CD4 Median | Impacts windows longer than |
|---|---|---|
| >500 | 1.5 | 3 |
| 350-500 | 4 | 8 |
| 200-350 | 8 | 16 |
Degree of impact will depend on how much longer windows are than 2x the CD4-based median
What is happening with the other 28%?
Distribution of time of CD4 measurement (x-axis, in days since diagnosis) and CD4 counts (colors) among the 838 individuals who did not have a CD4 count within 30 days.
High CD4s in delayed measurement groups may reflect initiation of treatment
Scatterplot of first CD4 count versus infection window length, among CD4-eligible cases (N=2178). Panels are testing status (columns) and MSM status (rows).
CD4 distribution density by testing history status (colors) and MSM status (panels).
Never-testers have CD4 distributions that are much more skewed towards low CD4.
CD4 distributions by testing history status (panels) and MSM vs non-MSM status (colors)
Never-testers with high CD4 are where the CD4 Case will have greatest impact. Never-testers with CD4 200-350 will have minimal impact.
| CD4 Category | CD4 Median | Impacts windows longer than |
|---|---|---|
| >500 | 1.5 | 3 |
| 350-500 | 4 | 8 |
| 200-350 | 8 | 16 |
The lowest-impact group are the CD4 250-300 cases with the longest windows
Median infection point = time by with 50% of infection probability has occurred
Among all cases with testing history (N=3016), average median infection points under the Base Case (orange) and CD4 Case (green), by CD4 bin.
More details included in an appendix slide
Among impacted cases (N=296), differences in the median infection points under the Base Case versus CD4 Case. Lines indicate the 50% percentile. The tall bins reflect the never-testers. Their 9-year median decreases to 8 years for CD4 200-450 (difference=1 year), to 4 years for CD4 350-500 (difference=5 years), and 1.5 years for CD4>500 (difference=7.5).
50th percentile decrease is larger for MSM (2.34 years) than for non-MSM (1.94 years)
1 year after diagnosis
| Population | % Undx at 1 year, Base Case | % Undx at 1 Year, CD4 Case | Difference | Percent Change |
|---|---|---|---|---|
| Total | 40.8 | 39.4 | 1.4 | 3.4 |
| MSM | 33.1 | 31.9 | 1.2 | 3.6 |
| non-MSM | 64.3 | 62.0 | 2.3 | 3.6 |
5 years after diagnosis
| Population | % Undx at 5 years, Base Case | % Undx at 5 Years, CD4 Case | Difference | Percent Change |
|---|---|---|---|---|
| Total | 16.4 | 15.0 | 1.4 | 8.5 |
| MSM | 11.2 | 10.2 | 1.0 | 8.9 |
| non-MSM | 32.0 | 29.7 | 2.3 | 7.2 |
| Population | Mean time undx, Base Case | Mean time undx, CD4 Case | Difference | Percent Change |
|---|---|---|---|---|
| MSM | 1.829 | 1.717 | 0.1122 | 6.13 |
| non-MSM | 4.378 | 4.127 | 0.2511 | 5.74 |
TID actually changes by 0.39 more percentage points for MSM than non-MSM
MSM
Time from infection to diagnosis: probability curve (top) and undiagnosed fraction curve (bottom)
non-MSM
Time from infection to diagnosis: probability curve (top) and undiagnosed fraction curve (bottom)
| Population | Base Case | CD4 Case | Difference | Percent Change |
|---|---|---|---|---|
| Total | 1319.0 | 1247.0 | 72.0 | 5.5 |
| MSM | 604.7 | 568.4 | 36.3 | 6.0 |
| non-MSM | 714.3 | 678.2 | 36.1 | 5.1 |
Subgroup decreases closely parallel the decreases in mean undiagnosed time (6.13% for MSM and 5.74% for non-MSM)
| Population | Base Case | CD4 Case | Absolute Difference | Percent Change |
|---|---|---|---|---|
| Total | 9.4 | 8.9 | 0.5 | 5.3 |
| MSM | 6.2 | 5.8 | 0.4 | 6.5 |
| non-MSM | 17.1 | 16.4 | 0.7 | 4.0 |
The fractions take into account diagnosed PLWH. Since the Base Case undiagnosed fraction is much higher for non-MSM, it is less sensitive than the MSM fraction to the CD4 Case's decrease of about 36 undiagnosed cases.
| Window Length | If CD4 unknown, infection probability is mostly: | CD4=Low | CD4=High |
|---|---|---|---|
| Short | Recent | Recent (fast progressor?) | Recent |
| Long | Non-recent | Non-recent | Recent |
In WA, only 10% of cases with testing history had infection windows that indicated less probability of recent infection than indicated by their CD4 count
We expected to see greater impact in non-MSM than MSM
We prioritize testing history data
We use CD4 conservatively
CD4 in cases with missing testing history
Multiple markers
MSM are 66% of all cases.
Recall that never-testers get a window that is either age-16 or 18 years.
Median infection point = time prior to dx within which 50% of infection probability occurs
| CD4 Bin | CD4 Bin Size | Number Impacted | % of CD4 Bin Impacted | Base Case Median | CD4 Case Median | Difference | Percent Change | Proportion in CD4 Bin |
|---|---|---|---|---|---|---|---|---|
| [0,200) | 582 | 0.0 | 0.0 | 4.8 | 4.8 | 0.0 | 0.0 | 0.2 |
| [200,350) | 423 | 58.0 | 13.7 | 2.6 | 2.5 | 0.1 | 3.8 | 0.1 |
| [350,500) | 482 | 66.0 | 13.7 | 1.8 | 1.3 | 0.5 | 27.8 | 0.2 |
| [500,2e+03] | 691 | 172.0 | 24.9 | 1.5 | 0.7 | 0.8 | 53.3 | 0.2 |
The impacted cases represent (172+66+58)/3016 = 10% of the cases contributing testing histories.
| Mode | CD4 Bin | CD4 Bin Size | Number Impacted | % of CD4 Bin Impacted | Base Case Median | CD4 Case Median | Difference | Percent Change |
|---|---|---|---|---|---|---|---|---|
| MSM | [0,200) | 369 | 0.0 | 0.0 | 4.0 | 4.0 | 0.0 | 0.0 |
| MSM | [200,350) | 317 | 24.0 | 7.6 | 1.9 | 1.8 | 0.1 | 5.3 |
| MSM | [350,500) | 396 | 35.0 | 8.8 | 1.3 | 1.0 | 0.3 | 23.1 |
| MSM | [500,2e+03] | 576 | 112.0 | 19.4 | 1.3 | 0.6 | 0.7 | 53.8 |
| non-MSM | [0,200) | 213 | 0.0 | 0.0 | 6.1 | 6.1 | 0.0 | 0.0 |
| non-MSM | [200,350) | 106 | 34.0 | 32.1 | 4.7 | 4.4 | 0.3 | 6.4 |
| non-MSM | [350,500) | 86 | 31.0 | 36.0 | 3.9 | 2.3 | 1.6 | 41.0 |
| non-MSM | [500,2e+03] | 115 | 60.0 | 52.2 | 2.9 | 1.1 | 1.8 | 62.1 |
Among all cases with testing history (N=3016), median infection points by Case and MSM status. The impacted MSM are 7% of MSM testing histories, whereas the impacted non-MSM are 17% of all testing histories.